Nato disunity was on full display on the opening day of the alliance’s summit in London as the French president, Emmanuel Macron, accused Turkey of colluding with Islamic State proxies while Donald Trump described Macron’s criticisms of Nato’s “brain death” as insulting and “very, very nasty”.

Trump also kept up his demand that “delinquent” Nato states boost their defence spending, warning if they did not do so he would consider imposing US trade sanctions.

The sense of disarray, reflecting wider differences about Nato’s future post-cold war purpose, emerged through a series of revealing rolling press conferences hosted by Trump.

Late on Tuesday, in a further sign of disunity, footage emerged from a Buckingham Palace reception of leaders including Macron, the British summit host, Boris Johnson, and the Canadian prime minister Justin Trudeau appearing to mock Trump’s lengthy media appearances.

Johnson largely kept a low profile, but convened a meeting in Downing Street in an effort to forge a common European-Turkish approach to the crisis in north-east Syria where tens of thousands of Syrian Kurds have been displaced because of the October invasion by Turkey and its proxies.

Macron’s original condemnation of Nato’s “brain death” stemmed from his anger at the lack of any Turkish cooperation with the rest of Nato over the invasion. Only Trump was consulted; he gave a green light that led to a massive political backlash in the US.

Macron on Tuesday repeatedly warned that Isis was making a comeback in Syria because of the Turkish invasion since it had weakened the mainly Kurdish Syrian Defence Forces, including the YPD fighters, that have formed the backbone of the fight against Isis. At one point Macron accused Turkey of sometimes working with Isis proxies.

Macron said he supported Nato developing wider goals including combating terrorism but said: “I am sorry we do not have the same definition of terrorism around the table. When I look at Turkey, they now are fighting against those who fight with us, who fought with us, shoulder to shoulder, against Isis. And sometimes they work with Isis proxies.” Turkey has to end its ambiguities towards these groups, he said.

He added: “I understand they now want to block all the declarations of this summit unless we agree their definition of terrorism. It is not our definition.”

The French president asked how it was possible to be a member of the Nato alliance and for Turkey to purchase the Russian S-400 air defence system. “Technically it is not possible,” he said.

Macron, in common with most Nato states’ leaders, maintains that a Russian defence system inside Nato will expose its military hardware, including the F-35 fighter jets, to Russian military intelligence.

Pressed by a reporter about whether the US was going to sanction Turkey for buying the S-400 as the US Congress was demanding, Trump said he was looking at the issue.

He then claimed, incorrectly, that Turkey had been forced into looking at the S-400 because Barack Obama had refused to let Turkey buy the US patriot defence system. “Turkey for a long period of time wanted very much to buy the Patriot system,” Trump said. Obama, he said, “wouldn’t sell” it.

In fact the Obama administration offered the weapon to Turkey repeatedly but Erdoğan refused because the US deal did not include the Patriot’s underlying technology.

After Trump’s defence of the Turkish position, Macron interjected. “It’s their own decision,” he said of Turkey, adding that Europe had also offered to sell Erdoğan an air-defence system. “Even having a European option, totally compliant with Nato, they decided not to be compliant with Nato.”

Trump then asked Macron whether he would take any of the foreign fighters that America had captured in Syria and Iraq. Trump said “We have a tremendous amount of captured fighters in Syria under lock and key, mainly from Europe. Would you like some nice Isis fighters? I could give them to you. You can take everyone you want.”

When Macron replied in a generality about the future status of Isis terrorists, Trump said: “That is why he is such a great politician. That is one of the greatest non-answers I have heard and that’s OK.”

As the tense exchanges continued Macron said: “Let’s be serious. It is true you have fighters coming from Europe. But it’s a minority problem of the overall problem we have. And I think the number one priority because it is not yet finished is to get rid of Isis.”

At an earlier press conference Trump had been ruder about Macron, saying his remarks about Nato being brain dead were “very, very nasty” comments.

“I think that’s insulting to a lot of different forces,” Trump said. “You just can’t go around making statements like that about Nato. It’s very disrespectful.”

Trump has himself once called Nato obsolete.

Macron has argued ever since the Turkish invasion of north-east Syria in October that the move was a disastrous distraction from the continuing priority of defeating Isis. He was also furious that the US started to withdraw all its remaining 500 troops from the area, effectively handing over airbases to Russia.

In an attempt to show his solidarity with the Syrian Kurds, Macron has also hosted political leaders of the Syrian YPD in Paris, praising them for the sacrifices they had made to defeat Isis.

Although Trump frequently praises Erdoğan, other members of the administration are more critical. The US defence secretary, Mark Esper, in an interview with Reuters agreed with Macron that Nato cannot label the YPD as a terrorist group. He said: “The message to Turkey … is we need to move forward on these response plans and it can’t be held up by their own particular concerns,” Esper said as he flew to London.

“Alliance unity, alliance readiness, means that you focus on the bigger issues – the bigger issue being the readiness of the [Nato] alliance. And not everybody’s willing to sign up to their agenda. Not everybody sees the threats that they see.”